When President Reagan was shot by John Hinckley Jr., in March 1981, the executive branch failed to invoke the 25th Amendment, which would have made Vice-President George Bush the acting president until Reagan could resume his duties. This compelling report documents the severity of the chief executive's injury, which the White House concealed from the public. Abrams, a Stanford University medical school professor, dramatically depicts the dangerous, sometimes farcical confusion in the aftermath of the shooting. James Baker, Edwin Meese and Michael Deaver ran the White House; ``they were the president,'' quips Abrams. While Soviet troops seemed poised to invade Poland, Secretary of State Alexander Haig and Secretary of Defense Caspar Weinberger jockeyed for power and squabbled over the alert status of U.S. forces worldwide. In a disturbing book that sounds an important warning, Abrams proposes guidelines for swift, effective action when a president is incapacitated. Photos. (Feb.)